"You need to assume an infinite amount "
If infinite independent factors were real, normal curve would have explained everything. Unfortunately, there is always "fat tail" phenomenon, which indicates only finite factors in the real world.
Also, be careful George. You need to assume an infinite amount of real numbers in order to calculate that integral
]]>I recently encounter an interesting task on studying fund rating methodologies. And I fund Lipper's Preservation Measure is
Sum(Min(0,ri))/T or Sum(Min(0,ri))/N*(T/N)
What it actually does is turn all the positive return r's to 0 and compute the average.
If we assume r normally distributed as N(u,s²)
The negative expectation can be modeled as E- =∫r*pdf dr over (-∞,0)
I came up with the answer
E-= u*N(-u/s)-(s/√2π)*exp(-u²/2s²)
But Michael Stutzer in his paper Mutual Fund Ratings: What is the Risk in Risk-Adjusted Fund Returns? derived an approximation as
Could you check this out and tell me why the difference? Thanks!
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